Transient conditions of two-phase air-water flow were numerically analyzed. The wave growth from a stratified flow regime in a horizontal duct was considered. Conservation equations were solved by finite difference method. The analyses on the onset of wave initiation was compared with the empirical correlations of other researchers. This analysis clarified that the Kelvin-Helmholtz instability criterion is valid only for waves with long wavelengths. Also, the required air velocity for the initiation of waves with short wave lengths is well below that defined by the Kelvin-Helmholtz instability relation.